In this lecture series I will first give a brief introduction to semidefinite programming and some of its applications. I will then focus on the class of feasible sets for such problems, so-called spectrahedra, and their linear projections. These sets are generalizations of polyhedra. Although there exists an exact definition, we so far do not have a satisfactory and easy-to-check characterization for them. The methods used in finding such characterizations come from convexity theory, optimization, algebra, algebraic geometry and functional analysis. This makes the area an exciting field of research, with many recent results, and many interesting results still to come.

The video for this talk should appear here if JavaScript is enabled.If it doesn't, something may have gone wrong with our embedded player.We'll get it fixed as soon as possible.